Postural stability can be threatened by the low-frequency motions in transport that are usually quantified by their root-mean-square (r.m.s.) acceleration. This study investigated how the stability of walking people depends on the waveform of 1- and 2-Hz mediolateral oscillations of the surface on which they walk. Walking on a treadmill, 20 subjects were perturbed by random oscillations of the treadmill with one-third octave bandwidths: different waveforms with the same r.m.s. acceleration and different waveforms with the same peak acceleration. Stability was measured subjectively and objectively by the velocity of the center of pressure in the mediolateral direction. Subjective and objective measures of walking instability increased with increasing r.m.s. acceleration of oscillations having the same peak acceleration. These same measures of instability were also affected by the peak acceleration when the r.m.s. magnitude of the oscillations was constant, especially with 1-Hz oscillations. It is concluded that r.m.s. measures of acceleration are insufficient to predict the postural stability of walking passengers exposed to mediolateral oscillations and that peaks in the oscillations should also be taken into account.